BÄCKLUND TRANSFORMATIONS FOR NON-COMMUTATIVE ANTI-SELF-DUAL YANG–MILLS EQUATIONS
BÄCKLUND TRANSFORMATIONS FOR NON-COMMUTATIVE ANTI-SELF-DUAL YANG–MILLS EQUATIONS
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DOI：
10.1017/s0017089508004801
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发表时间：
2007-09
影响因子：
0.5
通讯作者：
C. Gilson;M. Hamanaka;J. Nimmo
中科院分区：
文献类型：
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作者：
C. Gilson;M. Hamanaka;J. Nimmo
摘要 我们提出了非交换反自对偶 Yang-Mills 方程的 Bäcklund 变换，其中规范组为 G = GL(2)，并使用它从简单的种子解生成一系列精确解。这种方法生成的解以准行列式表示，属于 Atiyah-Ward ansatz 的非交换版本。在交换极限下，我们的结果与 Corrigan、Fairlie、Yates 和 Goddard 的结果一致。
Abstract We present Bäcklund transformations for the non-commutative anti-self-dual Yang–Mills equations where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasi-determinants and belong to a non-commutative version of the Atiyah–Ward ansatz. In the commutative limit, our results coincide with those by Corrigan, Fairlie, Yates and Goddard.